245,693 research outputs found
Incremental, Inductive Coverability
We give an incremental, inductive (IC3) procedure to check coverability of
well-structured transition systems. Our procedure generalizes the IC3 procedure
for safety verification that has been successfully applied in finite-state
hardware verification to infinite-state well-structured transition systems. We
show that our procedure is sound, complete, and terminating for downward-finite
well-structured transition systems---where each state has a finite number of
states below it---a class that contains extensions of Petri nets, broadcast
protocols, and lossy channel systems.
We have implemented our algorithm for checking coverability of Petri nets. We
describe how the algorithm can be efficiently implemented without the use of
SMT solvers. Our experiments on standard Petri net benchmarks show that IC3 is
competitive with state-of-the-art implementations for coverability based on
symbolic backward analysis or expand-enlarge-and-check algorithms both in time
taken and space usage.Comment: Non-reviewed version, original version submitted to CAV 2013; this is
a revised version, containing more experimental results and some correction
Parameterized Verification of Graph Transformation Systems with Whole Neighbourhood Operations
We introduce a new class of graph transformation systems in which rewrite
rules can be guarded by universally quantified conditions on the neighbourhood
of nodes. These conditions are defined via special graph patterns which may be
transformed by the rule as well. For the new class for graph rewrite rules, we
provide a symbolic procedure working on minimal representations of upward
closed sets of configurations. We prove correctness and effectiveness of the
procedure by a categorical presentation of rewrite rules as well as the
involved order, and using results for well-structured transition systems. We
apply the resulting procedure to the analysis of the Distributed Dining
Philosophers protocol on an arbitrary network structure.Comment: Extended version of a submittion accepted at RP'14 Worksho
Reachability Analysis of Time Basic Petri Nets: a Time Coverage Approach
We introduce a technique for reachability analysis of Time-Basic (TB) Petri
nets, a powerful formalism for real- time systems where time constraints are
expressed as intervals, representing possible transition firing times, whose
bounds are functions of marking's time description. The technique consists of
building a symbolic reachability graph relying on a sort of time coverage, and
overcomes the limitations of the only available analyzer for TB nets, based in
turn on a time-bounded inspection of a (possibly infinite) reachability-tree.
The graph construction algorithm has been automated by a tool-set, briefly
described in the paper together with its main functionality and analysis
capability. A running example is used throughout the paper to sketch the
symbolic graph construction. A use case describing a small real system - that
the running example is an excerpt from - has been employed to benchmark the
technique and the tool-set. The main outcome of this test are also presented in
the paper. Ongoing work, in the perspective of integrating with a
model-checking engine, is shortly discussed.Comment: 8 pages, submitted to conference for publicatio
Long-Term Average Cost in Featured Transition Systems
A software product line is a family of software products that share a common
set of mandatory features and whose individual products are differentiated by
their variable (optional or alternative) features. Family-based analysis of
software product lines takes as input a single model of a complete product line
and analyzes all its products at the same time. As the number of products in a
software product line may be large, this is generally preferable to analyzing
each product on its own. Family-based analysis, however, requires that standard
algorithms be adapted to accomodate variability.
In this paper we adapt the standard algorithm for computing limit average
cost of a weighted transition system to software product lines. Limit average
is a useful and popular measure for the long-term average behavior of a quality
attribute such as performance or energy consumption, but has hitherto not been
available for family-based analysis of software product lines. Our algorithm
operates on weighted featured transition systems, at a symbolic level, and
computes limit average cost for all products in a software product line at the
same time. We have implemented the algorithm and evaluated it on several
examples
The Fluctuation Theorem as a Gibbs Property
Common ground to recent studies exploiting relations between dynamical
systems and non-equilibrium statistical mechanics is, so we argue, the standard
Gibbs formalism applied on the level of space-time histories. The assumptions
(chaoticity principle) underlying the Gallavotti-Cohen fluctuation theorem make
it possible, using symbolic dynamics, to employ the theory of one-dimensional
lattice spin systems. The Kurchan and Lebowitz-Spohn analysis of this
fluctuation theorem for stochastic dynamics can be restated on the level of the
space-time measure which is a Gibbs measure for an interaction determined by
the transition probabilities. In this note we understand the fluctuation
theorem as a Gibbs property as it follows from the very definition of Gibbs
state. We give a local version of the fluctuation theorem in the Gibbsian
context and we derive from this a version also for some class of spatially
extended stochastic dynamics
Symbolic dynamics techniques for complex systems: Application to share price dynamics
The symbolic dynamics technique is well known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully applied to time series generated by complex systems of much higher dimensionality. Our main example is the investigation of share price returns in a coarse-grained way. A nontrivial spectrum of RĂ©nyi entropies is found. We study how the spectrum depends on the time scale of returns, the sector of stocks considered, as well as the number of symbols used for the symbolic description. Overall our analysis confirms that in the symbol space transition probabilities of observed share price returns depend on the entire history of previous symbols, thus emphasizing the need for a modelling based on non-Markovian stochastic processes. Our method allows for quantitative comparisons of entirely different complex systems, for example the statistics of symbol sequences generated by share price returns using 4 symbols can be compared with that of genomic sequences
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